Re: are Real Numbers evil? The answer(?).

> It sounds as if you are worried about irrational
> numbers and all kinds of monsters creeping in
> when you do geometric operations with real numbers,
> even if you started out with rational numbers.

Yes you are right. I want a finite, complete model not
extensible any more. Its size can be any integer
number of _given_ size, but it must be finite.
No infinity of any kind, no extension in any direction,
but rules how to handle the outer "borders" instead.
Full discrete complete model of 3D space with
elements in it and of limited size.
I have the feeling, that what I am seeking for
can't be described in terms usually used to
describe 3D space because it should express
a new kind of understanding of 3D space.
That's maybe the core of the difficulty
to talk about it.


> So, it would seem that sci.math is the correct
> newsgroup to ask this on, but all you will get
> is a lot of insult from arrogant people.

I have read on sci.math that very good mathematicians
don't post to it (Re: Your favorite troll warning signs,
Ross A. Finlayson June 02, 2005 06:35 :
"Most of the high powered mathematicians do not post
to sci.math. It might sully their reputation." )
Any hints how to reach them anyway?


> Instead, can you answer why you think a voxel
> model isn't enough for your discrete needs? What
> do you think your discrete and finite model should
> provide in addition to a basic cellular model?

I was not aware of voxel modelling, so thank
to the posters who directed me to it, but as it is
also based on the understanding of 3D
space as it currently is, it wan't probably
help to find what I am seeking for.

Below what I have posted to sci.math on June 1
and have not yet got any reply on was:

"I am looking for a discrete
"algebra of a 3D grid"
able to perform as follows:

- each single cube of the grid can be
empty or contain an element which
can have a finite number of properties.
- a set of adjacent cubes containing
elements can be moved around
within the grid (translation) in any
direction out of a finite set of possible
directions.
- any set of adjacent cubes containing
elements can be turned within the grid
(rotation) around any direction out of a
finite set of possible
directions and by any angle out of
a finite set of possible angles.
- applying any of the translation and
rotation operations keeps
the geometrical shape of the set
of the elements as close to each
other as possible (in terms of
continuous 3D shape in XYZ
coordinate system)
- applying any sequence of translations
and rotations doesn't change the
geometrical shape of the set
of the elements if compared to some
initial or intermediate shape if the
geometrical orientation of the set
is the same as the orientation
at the initial or intermediate state.
- there is no other information about a
set of elements available in the algebra
as that provided by properties of a single
element beeing part of the set i.e.
the properties of the adjacent elements
decide if a single element is part of a set
or not.
- the properies of the element can be
expressed in terms of a set of integer
numbers.
- the "coordinates" of a single cube
in the grid can be addressed by a
triple of integer numbers beeing the
x,y,z coordinates of the cube.

Is there anything like that already known?

Any hints are appreciated.
"

Claudio


<examachine@xxxxxxxxx> schrieb im Newsbeitrag
news:1117748965.058372.73810@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Claudio Grondi wrote:
> > > I don't quite see what you want.
> > That's the problem...
> > If I were able to express it better
> > I would sure do, but I'm not (yet?).
> > But if I really were, I would probably
> > have already also most of the answer,
> > so there would be no need for asking
> > a question and time for writing an
> > announcement instead.
> >
> > > Isn't using Z^3 enough for you? You seem to be asking just voxels. :)
> > >
> > > You have to state a concrete example, what do you want to rotate, how
> > > do you want to rotate, what do you think is not addressed, etc. etc.
> > I am not down to such details - just
> > thought, that if someone had done
> > already what I have asked for, he will
> > see my posting and let me know about
> > existing work.
> > I haven't got such reply, so I wrote the best
> > fitting answer to my original posting
> > myself after doing some more research work
> > with Google and Co.
> >
> > Currently it appears to me, that it is not
> > possible to talk here about 3D without
> > using for it a real number based coordinate
> > system approach, so I posted to the wrong
> > newsgroup asking what I have asked for.
> >
> > Thank you for your replies, anyway.
>
> It sounds as if you are worried about irrational
> numbers and all kinds of monsters creeping in
> when you do geometric operations with real numbers,
> even if you started out with rational numbers.
>
> So, it would seem that sci.math is the correct
> newsgroup to ask this on, but all you will get
> is a lot of insult from arrogant people.
>
> Instead, can you answer why you think a voxel
> model isn't enough for your discrete needs? What
> do you think your discrete and finite model should
> provide in addition to a basic cellular model?
>
> Regards,
>
> --
> Eray
>


.

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